Question

A stationary source is emitting sound at a fixed frequency $f_0$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars in $1.2$ of $f_0$. What is the difference in the speed of the cars (in km per hour) to nearest integer? The cars are moving at constant speeds much smaller that the speed of sound which is $330m{s}^{-1}$

• A. $2$
• B. $3$
• C. $5$
• D. $7$

Answer 1

Answer: (D)

$7$

Let the speed of the cars be $v_1$ and $v_2$.

Frequency received by the car, $f_1=\frac{v}{v-v_1}{f}_0$

Frequency reflected by car, $f_2=\left(\frac{v+v_2}{v}\right)\left(\frac{v}{v-v_1}\right)f_0$

$\Delta f=f_2^{\prime }-f_1=(\frac{v+v_2}{v-v_2}-\frac{v+v_1}{v-v_1})f_2$

Solving we get,

$\Delta f=\frac{(2v_2-v_2)f_0}{v}$

Equating this to $\frac{1.2f_0}{100}$, we get,

$v_2-v_1=7$